Takesaki, Masamichi Theory of operator algebras I. (English) Zbl 0436.46043 New York, Heidelberg, Berlin: Springer-Verlag. VII, 415 p. DM 79.00; $ 44.30 (1979). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 10 ReviewsCited in 595 Documents MathOverflow Questions: Name for a set of elements that fully determine a morphism MSC: 46L05 General theory of \(C^*\)-algebras 46-02 Research exposition (monographs, survey articles) pertaining to functional analysis 46L10 General theory of von Neumann algebras 46L35 Classifications of \(C^*\)-algebras 46L45 Decomposition theory for \(C^*\)-algebras 46L51 Noncommutative measure and integration 46L53 Noncommutative probability and statistics 46L54 Free probability and free operator algebras Keywords:Gelfand representation; automatic continuity; cone of positive elements; bounded approximate unit; Gelfand-Naimark-Segal construction; asymmetric Riesz decomposition; von Neumann’s locally convex operator topologies; double commutant; predual; Kaplansky’s density theorem; Kadison’s transitivity theorem; non-commutative analogues of Lusin’s and Egorov’s theorems; universal enveloping von Neumann algebra; polar decomposition of functionals; Arens-Mackey topology; universal measurability; completely positive maps; Tomita’s commutant theorem; direct integrals; desintegration of von Neumann algebras; Murray-von Neumann dimension theory; multiplicities; factors; maximal ideal space PDF BibTeX XML OpenURL